José Luis Gómez-Muñoz

The Simpsons and Mathematics 3

José Luis Gómez-Muñoz http://homepage.cem.itesm.mx/lgomez/

Read this article:

Sarah J Greenwald, Andrew Nestler. "r dr r: ENGAGING STUDENTS WITH SIGNIFICANT MATHEMATICAL CONTENT FROM THE SIMPSONS" Primus : Problems, Resources, and Issues in Mathematics Undergraduate Studies. Mar 2004. Volume 14, Issue 1; pages 29-39
Answer the following questions in the proper forum of the ELECTRONIC DISCUSSION BOARD:

WARNING: It might be difficult to understand some of the jokes, because some of them cannot be translated to Spanish (or any other language). And it is even worse; some of the jokes are funny for USA people who is more than 35 years old, because they refer to old movies or old TV-series like "The Wizard Of Oz", the original version of "Twilight Zone" ("Dimensión Desconocida") and "Tron". Therefore, in order to understand the jokes you might need some help from your parents!
1. Read the section "3. 3-D Homer" which starts in the page 32 of the article. Have you seen the chapter ("Homer³") that is described in that section?
2. Answer exercises 1a, 1b and 1c in page 33 of the article.
3. Answer exercise 2 in page 34 of the article.
4. Comment on a four-dimensional Homer, as mentioned in the paragraph that starts at the eleventh row in page 35 of the article.
5. Did you know that "The Simpsons" has some allusions to Math and Science?
6. Do you like "The Simpsons"? Why?
7. Do you think that "The Simpsons" is educative?
8. Compare your answers with the answers of your classmates in the ELECTRONIC DISCUSSION BOARD. Are there other points of view? Do you think they could be right? Why?.

Author: José Luis Gómez-Muñoz

jose.luis.gomez@itesm.mx

Students' Answers:

Current Forum: The Simpsons	Read 41 times
Date: Mon Aug 16, 2004 11:31 pm
Author: Heredia Soriano, Francisco Javier <ya_viene_mandinga@yahoo.com>
Subject: Re: Write here your answers to the Discussion Activity


fRANCISCO hEREDIA 460084 Answer the following questions in the proper forum of the ELECTRONIC DISCUSSION BOARD: Read the section "3. 3-D Homer" which starts in the page 32 of the article. Have you seen the chapter ("Homer3") that is described in that section? Answer exercises 1a, 1b and 1c in page 33 of the article. 1a.- Homer looks very diferent in 2-d than in 3D because of the shaded texture. In the second place, we have a contrast with the background surface, as we have a propagation of the axis instead of having furniture simulating 3d positioning. 1b.-The fact that they dont present shades. They never walk closer or farther from the screen, they always walk on the y axis. 1c.- Sometimes they do walk in and out from the screen . I remember the chapter when Mr Burns was confused with an alien and he came out of the woods betwee the trees. In a 2-d world if would not have been possible to be "behind " the tree. Another example could be when Bart and Lisa entered the television and the Itchy & Scratchy show. When Homer was watchign Tv, he sat on the couch while they were inside the screen yelling at him, we can notice how the TV is showed as three-dimensional space and at the back there is the couch and Homer. Answer exercise 2 in page 34 of the article. Marge, I am stuck in a world where I can see as far as the eye can. There are no limits and I ca walk around other objects. I cannot go through them but I can go up, down and around. I can also see that my belly comes out from me to the front. I knew I was fat but not that fat! I can walk left,right, forward and backwards. Help me Marge! This place is scary! Comment on a four-dimensional Homer, as mentioned in the paragraph that starts at the eleventh row in page 35 of the article. I think the fourth dimension is time. Something might have width, height and lenght. But just suppose that thing only lasts for 1/100000 second . Would that object be real? After it appears and disappers, I can go through the same spae it was occupying and nothign would happen. NOt only volume is important but the endurance in time. Thigns occupy a place in space and time. Did you know that "The Simpsons" has some allusions to Math and Science? I didn't know it as that serious. I thought those were only mere jokes. Do you like "The Simpsons"? Why? I do like them very much. They show a funny side about american society. And I guess they have some characteristics about everyone. That is why they are so popular around the world, because people feel identified. Do you think that "The Simpsons" is educative? Not much. But a little. they are very funny though. Compare your answers with the answers of your classmates in the ELECTRONIC DISCUSSION BOARD. Are there other points of view? Do you think they could be right? Why?. n/a

Current Forum: The Simpsons	Read 30 times
Date: Wed Aug 18, 2004 6:26 am
Author: Esquivel Acosta, Jaime Alberto <00467889@academ01.itesm.mx>
Subject: Re: Write here your answers to the Discussion Activity


467889 Differences between 2D Homer and 3D Homer: • The shadows in 3D are easily seen; in 2D there is not too much shadowing. • The lighting in 3D is as the shadowing: easily to recognize. In 2D there is always the same lighting. Only in a few chapters, especially in Halloween some darker places. • You can compare the physical differences between a 3D cartoon and a 2D cartoon when Homer sticks his stomach in the 3D comparing it when Homer is at the hospital and the doctor sticks his stomach. Aspects that could be used to argue that the Simpsons live in a 2D world: • The way in which the body of the characters is drawn. • I really don’t find another aspect. Aspects that could be used to argue that the Simpsons live in a 3D world: • The way they move, for example when Homer enter to the tavern and ask for a beer, Moe takes the glass and moves it forward (x), then he slides it by the table (y) and when Homers catch it he lifts it (z). • When they are driving, or playing, etc. 4D Homer: • I really can’t imagine a 4D representation of anything, Maybe it could be understood if you think that the Simpsons live in a 3D representative world and Homer gets into a 4D representative dimension, but in a real space I think I could be difficult to imagine a 4D room, the only thing that I can imagine is the 3D shadow of a 4D object. Do you think that the Simpsons have some allusions to Math and science? • Before reading the article I really didn’t think of, but after that I guess you could find some of those mentioned allusions, even do I think is not what producers want you to see. Do you like the Simpsons? Why? • Yes I like them (especially Homer), because they give you some messages as: you could have fun from a typical day or situation, Luck exists, etc. and I guess everybody has a little of each character. Comparing answers: (There is only one message). Much of the answers are based in the same aspects but explained in different ways. I guess everyone in the classroom will answer: “yes I like the Simpsons because…” .

Current Forum: The Simpsons	Read 27 times
Date: Wed Aug 18, 2004 7:03 pm
Author: Estrada Benavides, Javier <A00460250@itesm.mx>
Subject: Re: Write here your answers to the Discussion Activity


Javier Estrada B. 460250 Read the section "3. 3-D Homer" which starts in the page 32 of the article. Have you seen the chapter ("Homer3") that is described in that section? Yes, I’ve seen it Answer exercises 1a, 1b and 1c in page 33 of the article. 1a. The differences are these: In some points like his nose and eyes we can see some type of a little 3D perspective (the curves make an effect like a cylinder, there is no effect like lighting; the perspective of depth isn’t clear, it uses only the size of the figures. The 3D world is totally different, it doesn’t need the size of things to get a perspective of depth; it has an effect of shadow in some parts of the figures which also mean depth, the light is different in many points of Hommer. 1b. In the supposedly 2-D world, what aspects could be used to argue that the Simpsons are living in a 2-D world? The effect of the hair and the shoes are completely flat, some cars have the same effect, and sometimes the look of Homer’s stomach 1c. In the supposedly 2-D world, what aspects could be used to argue that they are living in a 3-D world? (Hint: think about their movements and behaviors, the world that is represented, and the use of perspective in the bookcase and in the cube that Professor Prink drew.) When someone moves his hand/arm, the effect of the shape looks like a 3D model; sometimes they have an inclined view of some place, and it makes it all look like a 3D world. Answer exercise 2 in page 34 of the article. Exercise 2. Assume that the Simpsons really are 2-D creatures living in an x-y plane and that Homer is transformed into a 3-D creature. Though a 2-D Marge Simpson couldn't really understand the third dimension and would feel there isn't any room for another dimension, she could see weird behavior occurring that suggests the third dimension exists (for example the "wall" into which Homer disappeared). 2-D Marge wouldn't be able to comprehend the concept of depth or an entire 3-D Homer, since only 2-D pieces would make sense to her. Write a letter from 3-D Homer Simpson to his 2-D wife Marge which discusses his change from 2-D into 3-D. be sure to include mathematical explanations in addition to physical descriptions. Letter: This world is really strange! There is some kind of a dark figure of myself on the floor but I don’t know what it is, and the objects in here are very unfamiliar, they have the half of them in one color and the rest is in the color of my dark figure; I can walk in many more directions than we used to; everything is expanded through an extra axis apart from “x” and “y” and many objects look like made of cubes, balls and surfaces, it’s really strange, I don’t know how to move in here. Comment on a four-dimensional Homer, as mentioned in the paragraph that starts at the eleventh row in page 35 of the article. A 4D Homer would be like many things: We can start imaging a set of Homers through time in only one body and the fourth dimension would be the time, or we can talk about a transparent Homer and start talking about meta-physics. Did you know that "The Simpsons" has some allusions to Math and Science? No, I didn’t know that, until today. Do you like "The Simpsons"? Why? Yes, I like it, because it entertains you for a long while and it’s always creative. Do you think that "The Simpsons" is educative? I really don’t think that this show might be educative, because we would need and explanation of the things the show wanted to teach for every episode, just like this exercise. Compare your answers with the answers of your classmates in the ELECTRONIC DISCUSSION BOARD. Are there other points of view? Do you think they could be right? Why?. The first message also talks about time, and I think time is the right fourth dimension, just as he was saying, the object/thing must have a length defined in time units,

Current Forum: The Simpsons	Read 23 times
Date: Thu Aug 19, 2004 1:11 am
Author: Herrerías Aguilar, José Manuel <A00467790@itesm.mx>
Subject: Re: Write here your answers to the Discussion Activity


exercise 1a. The main diference between the 2d and the 3d homer is that the 2d homer is drawn by hand and the 3d is generated by computer, the 3d homer has shadows and ligthings the 2d dont. also the enviroment is generated by computer in the 3d view. exercise 1b. The main aspect are the enviroments like the streets, also the faces of the characters they are always showed in a front or in a sided perspective. exercise 1c.We can see a 3d behaivor when they do wild stuffs and move all around a plce because they go foward and backward and left and right so its show as if the where in a 3d world. Exercise 2. I think that neither Marge nor we can understand easily the problem of adding another dimension to our enviroment.Simply we couldnt understand the things taht would be arround us nor control our body. Comment on a four dimensional Homer. I think that if we think in the idea that the simpsons live on a 3d world and homer jumped to a 4d world we could think that as we live outside the tv we might live on a 5d world. Did you know that "The Simpsons" has some allusions to Math and Science? Yes in fact they do some other alusions to science that arent mentioned in the article. Do you like "The Simpsons"? Why? Yes, who doesnt in like it because you can see the same episode a hundred times and it continues entertaining you. Do you think that "The Simpsons" is educative? I think that its very educative in the aspects of popular culture i have learned a lot of the american culture just watching the simpsons. Compare your answers with the answers of your classmates in the ELECTRONIC DISCUSSION BOARD. Are there other points of view? Do you think they could be right? Why?. I think that all of them are right in their points, and all of them has a very similar point of view of the article.

Current Forum: The Simpsons	Read 18 times
Date: Thu Aug 19, 2004 7:53 am
Author: Martínez Anaya, Andrés Humberto <A00467909@itesm.mx>
Subject: Re: Write here your answers to the Discussion Activity


1.- Read the section "3. 3-D Homer" which starts in the page 32 of the article. Have you seen the chapter ("Homer3") that is described in that section? Yes, I have seen that chapter, but I saw it too monthas ago, and I don´t remenber all the chapter. 2.- Answer exercises 1a, 1b and 1c in page 33 of the article. Exercise 1a. Discuss the differences between 2-D and 3-D Homer. be sure to relate shadowing, lighting and physical differences in the 2-D and 3-D worlds to an explanation of how these differences give the appearance of added depth. Well Homer is very different in 3D, because in tha cartoon I never see the shadows of the characters, and the lighting is very low, but Homer in 3D seem to be a futuristic cartoon, because whe he touch his stomanch all his stomach move it like a wave in the sea. So you can see that Homer in the normal cartoon is a very simple draw that can be a very complicated draw in 3D. Exercise 1b. In the supposedly 2-D world, what aspects could be used to argue that the Simpsons are living in a 2-D world? That it is not much shadows in all the cartoon and the lighting is the same all the time, although you see depht in the cartoon is only a lie for your eyes, because all the cartoon is in 2D. Exercise 1c. In the supposedly 2-D world, what aspects could be used to argue that they are living in a 3-D world? (Hint: think about their movements and behaviors, the world that is represented, and the use of perspective in the bookcase and in the cube that Professor Prink drew.) The aspects to argue that The Simpsons are living in a 3D world are little. All their movements are in the same plane. and its very different the Homer in 3D than the 2D, and also when you see the cube that Professor Prink drew you can think that the simpsons are a 2D cartoon. Answer exercise 2 in page 34 of the article. Write a letter from 3-D Homer Simpson to his 2-D wife Marge which discusses his change from 2-D into 3-D. be sure to include mathematical explanations in addition to physical descriptions. Well my dear Marge I am in the third dimension and i am very defferent from the Homer you knew in my old world. Here all the things have depth and the ligting is very different from all the objects depending on the point that you are watching those objects. I have shadows in all my body. I fyou don´t understand me only watch the cube Professor Prink drew and try to touch the plane that is inside the blackboard. You can´t touch it, can you? well that plane is the 3D, and I am there. So help me to exit this place!!!!. 4.- Comment on a four-dimensional Homer, as mentioned in the paragraph that starts at the eleventh row in page 35 of the article. Well it is true that if you think that The Simpsons are a 3D cartoon, the Homer in 3D would be a Homer in 4D. But we can´t imagine the 4D so this is a simple probe that the simsons are a 2D cartoon, beause there´s nobody who can draw a 4D cartoon yet. Did you know that "The Simpsons" has some allusions to Math and Science? Well I have never herd that The simpsons has some allusions to Math and Science, but I think that if I analiza the cartoon maybe I found some of this allusions. Do you like "The Simpsons"? Why? Yes, I like it because they are funny and they criticaze all the defects in the american society, so I like they always say the true. Do you think that "The Simpsons" is educative? Well, I don´t think so because they are only a cartoon to fun people but they don´t try to be educative. Compare your answers with the answers of your classmates in the ELECTRONIC DISCUSSION BOARD. Are there other points of view? Do you think they could be right? Why?. Well I think that all the classmates have the same concepts of the simpsons bacause all like it. I think that the second comment is interesting because it is only posible to imagine a 3D shadow of a 4D object, but it´s impossible to imagine that object.

Current Forum: The Simpsons	Read 15 times
Date: Thu Aug 19, 2004 12:40 pm
Author: Tepoxteca Alvarez, Rodolfo <A00468235@itesm.mx>
Subject: Re: Write here your answers to the Discussion Activity


Answer exercises 1a, 1b and 1c in page 33 of the article. 1.a. Differences between 2d and 3d Homer Finally a Simpsons' character reflects light gradually. Homer's head reflects light because the lighting is up, but also this reflects go gradually descending because Homer's body is not as close to light source. The reflects descend until his feet where we appreciate shadows instead. At another moment of the episode he drools and his saliva gets to a fountain where there are fishes. When the drop contact the water we appreciate that the fishes are affected by the water movement and this is clearly in 3D 1.b. Simpsons in a 2D world It could be a 2D world because there are many scenes in which all the city meet and altough they are so close to each other they don't seem to occupy a space. The shadows they could have are only a black sketch of the character 1.c Simpsons in a 3D world The only evidence of this is the fact that they walk between planes. THey could be in a far away plane and run to a close-to-screen plane Answer exercise 2 in page 34 of the article. DeaR MaRge... About the world im now I feel so differenT BecaUsE whenEvEr I Walk I feel some beats on my Chest. If at home my heaRt poundS QUickly now i fEEl it(Now Homer feels the pound because his hearts is 3D too and it pounds in an axis perpendicular to his arms). I kicked a triangle-like object and it seemed to be DefoRmed in a particular way ( In this world when a object receive an external force it could be deformed by the 3 components of the force in a x, y and z axis) Comment on a four-dimensional Homer, as mentioned in the paragraph that starts at the eleventh row in page 35 of the article. of course a 4D object would be impossible to think... in our world. But in this hypotethical 3D world we may think of 4th dimension as mass, because here we can see that objects behave "normally" Did you know that "The Simpsons" has some allusions to Math and Science? Yes, because this is a cartoon that tries to reflect real life so I suppose that they had to use real mathematics and science laws Do you like "The Simpsons"? Why? Yep. THey try to recreate our world in a sarcastic way that is just hilarious. Do you think that "The Simpsons" is educative? Not too much. There are few episodes in which education is the main plot Compare your answers with the answers of your classmates in the ELECTRONIC DISCUSSION BOARD. Are there other points of view? Do you think they could be right? Why?.Everybody has their point of view, each one see things that the others don't so anybody is right

Current Forum: The Simpsons	Read 19 times
Date: Thu Aug 19, 2004 2:00 pm
Author: Gutiérrez Mercado, Jorge Victor <A00461454@itesm.mx>
Subject: Re: Write here your answers to the Discussion Activity


1. Read the section "3. 3-D Homer" which starts in the page 32 of the article. Have you seen the chapter ("Homer3") that is described in that section? Yes, its a very funny chapter. 2. Answer exercises 1a, 1b and 1c in page 33 of the article. - 1a Between 2-D and 3-D Homer are some significant differences. For example the shadows that Homer shows in the 3-D world could be considered rare or even unexistent in the 2-D world of “The Simpsons”. -1b In general, the drawing, the perspective that the drawer shows (in front or side). -1c When the characters are shown diagonally, when Bart and Lisa watch the T.V and some objects in the program (beers for example). 3. Answer exercise 2 in page 34 of the article. Dear Marge: I can’t really imagine were I am. The place is weird and I can move in more directions than on our world (we only move on “x” and “y” and here there is another direction, mmmmm, I think I can call it “z” ). There is a black thing following me. It looks like me!!. There are some stranges objects made of cubes, spheres and things I’ve never seen before. Help me Marge... Waaaaaaah! 4. Comment on a four-dimensional Homer, as mentioned in the paragraph that starts at the eleventh row in page 35 of the article. Its difficult to imagine a 4-D Homer, because the simple complexity of the 3-D world doesn’t allow us to imagine another dimension. Maybe the 4-D Homer can the Homer that are showed in the end of the chapter or an Homer that can travel between time or some other difficult things to explain. 5. Did you know that "The Simpsons" has some allusions to Math and Science? No, until I saw that chapter. The only thing related to Math and Science was that scientific (Frink), but it looks more like a joke, nothing serious. 6. Do you like “The Simpsons”? Why? Yes, because they show the life of a typical american family. Also because the characters and the stories are funny. It makes me laugh a lot. 7. Do you think that “The Simpsons” is educative? Sometimes, but not to much. Just life lessons. 8. Compare your answers with the answers of your classmates in the ELECTRONIC DISCUSSION BOARD. Are there other points of view? Do you think they could be right? Why? There are only a little bit of different points of view, but in general are likely the same, some are more explained and others are very short but clear.

Current Forum: The Simpsons	Read 19 times
Date: Thu Aug 19, 2004 2:40 pm
Author: Kumazawa Kuniyoshi, Oscar Yuki <A00460379@itesm.mx>
Subject: Re: Write here your answers to the Discussion Activity


1. Read the section "3. 3-D Homer" which starts in the page 32 of the article. Have you seen the chapter ("Homer3") that is described in that section? Yes, I have seen this episode. Quite funny indeed. 2. Answer exercises 1a, 1b and 1c in page 33 of the article. Homer gets in a really big trouble when he decides to adventure into the 3d world rather than enjoying a couple of home videos from Marge’s sisters. When Homer goes “^3”, his physical appearance and environment changes into a 3d world. Homer’s belly becomes a fat ellipsoid instead of a big circle. His complete body becomes rendered and with some artistic blurs and lightings, his display looks in three dimensions, even if it’s seen on TV. I believe that shadowing and lighting effects are the main factors of making Homer’s shape look as 3d considering the x, y and z translation, many could say that even in 2d there exists shadowing and lighting effects, but the mathematical shadowing and lighting is rather unique, and even if the colors of a brush and pencil match these effects, which is possible, easy sometimes, the x, y and z plane was so forced in Homer’s 3d world that it offered a great depth effect, showing again that creativity and talent can make any original 2d form a 3d shape. We could say that the Simpsons live in a 2d world because the shapes are art drawings, even in some episodes of the first season, some places were not colored and badly shaped looking definitely 2d, however, we could say in some way that the Simpson characters are walking in a 3d environment, even if they’re 2d, because, as the question suggested, they walk in the x, y and z plane even if we don’t notice it at first sight. There is a “Kwik E Mart” behind “Moe’s Bar”, and there is a “Springfield Elementary School” which must be placed using the x, y and z axis to locate it. It’s nearly impossible to put Springfield in the x and y axis. We need the z axis to place Bart behind Homer, or Homer’s left hand hitting Bart’s head while drinking some “Duff” with his right hand, so, we could say that “The Simpsons” are living in a 3d and 2d world. 3. Answer exercise 2 in page 34 of the article. Hi Marge, I’m feeling a little weird here. My body has turned into pieces of mathematical graphs and surfaces, what was once my head it has turned into a cylinder and a sphere, imagine that you draw a diamond shape in the blackboard. Now, draw another diamond shape behind it, join those edges and you will see like a figure jumping from the board, and well, imagine now that the diamond shape is my body…shadows and lighting effects forcing some depth, and we could say it’s 3-dimensional. 4. Comment on a four-dimensional Homer, as mentioned in the paragraph that starts at the eleventh row in page 35 of the article. Homer could really be in a 4 dimension instead of 3d, his real world could be the one in 3d and after crossing the wall Homer could be “^4”, quite interesting to think about it, maybe Homer’s shape would look like this in the real dimension, I believe that all dimensions are directly related, so Homer’s shape could really be in four dimensions in the Simpson world. 5. Did you know that "The Simpsons" has some allusions to Math and Science? I have noticed some math equations and allusions in some episodes, like Homer^3 and when Bart goes to some “genius school”. 6. Do you like "The Simpsons"? Why? I really like “The Simpsons” because this tv series makes smart jokes, and funny parodies to the real world. A breath of entertainment for our health. 7. Do you think that "The Simpsons" is educative? “The Simpsons” is educative because it shows many attractive concepts, and above all, it teaches with entertainment and funny jokes. A good way for children and adults to enjoy learning. 8. Compare your answers with the answers of your classmates in the ELECTRONIC DISCUSSION BOARD. Are there other points of view? Do you think they could be right? Why?. There are many POVs in the discussion board, it's really entertaining discussing these kinds of topics because we definitely need to focus and learn many things. Many answers could be right, because all of them have some correct points and comments. Good discussion.

Current Forum: The Simpsons	Read 10 times
Date: Thu Aug 19, 2004 7:48 pm
Author: Gallardo Vasconcelos, Luis Adrián <00456196@itesm.mx>
Subject: HOMER mmmmmmm ou


Read the section "3. 3-D Homer" which starts in the page 32 of the article. Have you seen the chapter ("Homer3") that is described in that section? No Answer exercises 1a, 1b and 1c in page 33 of the article. 1a. Ths small size of the "far away structures is represented far, bun in 2d they are just righ behinf, beside the light points are much more better represented 1b. They are every time in the same place and if they want to go out of the secreen that is imposoble. 1c. the 3-d aspect is a lot more comprehensible than some 2d, but some times is backwards so the main aspectos of a cartoon, is not releted to be a 2d that represents a 3d. Answer exercise 2 in page 34 of the article. Marge I can be in steped in the floor or in the walls, and even in the sealing and come back again to the floor, even thourg i can go as far as I can on any way, I can turn to the left and keep walkin, Turn to the left agan an go on in any direction I want, but I still can find my way back, so PEASE MARGE HEEELP MEEEEEEEE. ou!!!!. Comment on a four-dimensional Homer, as mentioned in the paragraph that starts at the eleventh row in page 35 of the article. I just can't imagine a fourth dimension, but i can only say that homer can be as fat and dumb as a fouth dimension can exist, so ther is always a posibility. Did you know that "The Simpsons" has some allusions to Math and Science? Ther is only some thing that alway can make you think a littlie more. Do you like "The Simpsons"? Why? I really don't , because I don't find them atractive. Do you think that "The Simpsons" is educative? there are a ot of thing in this cartoon that are not for children, and they cant realize that teri is an educative content in there because they just want to see something funny. Compare your answers with the answers of your classmates in the ELECTRONIC DISCUSSION BOARD. Are there other points of view? Do you think they could be right? Why?. Yes there are, and i think that anyone can imagine their own worl as any way they want.

Current Forum: The Simpsons	Read 10 times
Date: Thu Aug 19, 2004 8:53 pm
Author: Romero Tapia, Alfredo <fetus82@yahoo.com>
Subject: Re: Write here your answers to the Discussion Activity


1. Yes,it is one of the Halloween Specials. 2. I like more 3D Homer, because it looks more real, and the best part is when homer see his body and he realize that he is fat. b) The perspective is interest, but he is always on move only horizontally. c) The beer!! 3. Dear Marge: Im on a more interesting world! I think I am in another dimension, and the best of all are the donnuts!! But I dont like that big whole, that is taking me down, I think it wants to take me to another place, and the worst of all is that Im fat Marge, Im fat.. I know this has to be a bad joke from Bart.. Baaaart!!!! 4. I think its not possible, well, I cant imagine a 4th dimension, but it could be nice!! to travel to somewhere else, when ou want.. Homer will be always going to MOES! 5. Yes, I knew it, because i was an special where the artist show you how to make possible the SIMPSONS on al blank sheet. 6. I love it, because its a great example of an ordinary american family, and it is very funny to see ITCHY & SCRATCHY 7. Well, not al the chapters, but most of them cuz they treat themes like friendship. 8. It curious because there are all kind of answers, but its ok, cuz each person has his own ideas.

Current Forum: The Simpsons	Read 8 times
Date: Fri Aug 20, 2004 12:21 am
Author: Trejo Rodríguez, Daniel <al00926181@academ01.tol.itesm.mx>
Subject: Re: Write here your answers to the Discussion Activity


1.A Exist some differences between in Homer 2D and Homer 3D, the differences that I see are: The Homer 3D is more easy to see and analyze with the shadows, the homer in 2D is difficult because it has the same light. In the physic you can see a big difference about in the cartoons, in 3D the curves in general are used for made a species of cylinders. 1B The form that the body of cartoons are made, in structure, in movement, etc. The form that we use de axis. 1C The movement that Homer use. Moe, the barman, move the glass in one straight line. We can see that the movement are in the axis(x,y,z) in any. Example it can be when Lisa and Bart watch the T.V program. 2. Dear Marge, I´m feeling very rare, because this place has more size in all aspects, exist thing that I never seen, like a thing like me but is ever behind me, the persons call it shadow, I can move in all the directions, but is different, I can walk like rolling, This place cause me fair, because don´t exist limits, you have to see for understand this place, I miss you. 4.-PAGE 35 I think that 4D like or relative about time or revolutions. The object it can be real because in moments appears and are useful, but has a contradiction but in other moments doesn´t exist. 5.- Yes, I think that it was a incredible idea for the autor for show us that everything is possible, and the Simpsons are successful. 6.- I enjoy it very much, because is a critic about the simple American family, that lives in the middle of the economy in the U.S. 7.- Yes, all the chapters, all has your different and all identify with some. 8.- I see, that all has a similar ideas of they think about 4D and The Simpson, for all love this cartoon, and in the 4D I see that is difficult to imagine stay in other dimension and talk about this real dimension.

Current Forum: The Simpsons	Read 10 times
Date: Fri Aug 20, 2004 6:27 am
Author: Martínez Navarro, Edgar <A00460433@itesm.mx>
Subject: Re: Write here your answers to the Discussion Activity


1. Read the section "3. 3-D Homer" which starts in the page 32 of the article. Have you seen the chapter ("Homer3") that is described in that section? Yes, it was a Halloween special chapter. 2. Answer exercises 1a, 1b and 1c in page 33 of the article. 1a. 2-D Homer only needs to variables to exist (large and width), so if a light in any position bights in front of him, the shadow will be only a line with the size of the large or the width of Homer, meanwhile the shadow in the floor of the 3-D Homer has two variables. If we assume that 2-D Homer is the real one, Homer doesn’t have volume, so he isn’t fat. 1b. They live in 2-D World, all the things only have large and width. And Franky argued that he discovered the cube (3-D), so they really live in a flat world. 1c. In some chapters Matt Groening use isometric views, he tries two represent depth. The most common scene is the beginning of the program, when Marge and Maggie are driving to home, they change from 2-D to 3-D scheme. 3. Answer exercise 2 in page 34 of the article. Hi Marge: I suffered a little change, I can only see my breast, my legs and my arms and everything seems to be rounded. I don’t know what happened, but I made a theory that I grew a little bit. This theory is: You are tall and thin, but what happen if we add another portion of you and we get Homer-Depth. (Tall + Thin + Homer-Depth instead only Tall + Thin). You really don’t have a shadow, I have a 2-D one, it so strange. I’m in 3-D right now isn’t it to bad at all, I feel rounded and everything is clearer, you can see what you want with more details. Love you so much, Homer. 4. Comment on a four-dimensional Homer, as mentioned in the paragraph that starts at the eleventh row in page 35 of the article. A 4-D Homer existed at the end of the chapter, when he was in the real world, because he was under the effect of the time. He lived like we do everyday. 5. Did you know that "The Simpsons" has some allusions to Math and Science? No, it is so interesting that a regular program has science and math basis. 6. Do you like "The Simpsons"? Why? Yes, it is so simple, the creator is genius, and he has the fun in his blood. 7. Do you think that "The Simpsons" is educative? When I finished reading the lecture I have to answer with a yes. It’s incredible the basis that it has. Before, I always thought that “The Simpsons” was only sarcastic and hilarious way to see American life, but now it created science and math concept in my mind. 8. Compare your answers with the answers of your classmates in the ELECTRONIC DISCUSSION BOARD. Are there other points of view? Do you think they could be right? Why?. Yes, there are a lot of different points of view, because we answer this questionnaire with the previous knowledge that we have. We can’t be wrong, because we are only making suppositions of what we think, and each head is world, the only person that really knows how many planes do really they have, it’s Matt.

Current Forum: The Simpsons	Read 8 times
Date: Fri Aug 20, 2004 11:53 am
Author: Kumazawa Kuniyoshi, Oscar Yuki <A00460379@itesm.mx>
Subject: Re: Write here your answers to the Discussion Activity Reflection about last question


Well, being more specific with the last question, just as Francisco said, many of us learn a lot from the Simpsons because we kind of identify with these hilarious characters, so, if some episodes allude some math exercises, we could enjoy learning, also, about the 3D world, Francisco says that a 3d world could be present in the Simpsons like the Burn`s and Itchy and Scratchy episode mentioned, because there could be a 3d world inside a 2d world in the Simpsons.

Current Forum: The Simpsons	Read 6 times
Date: Fri Aug 20, 2004 2:00 pm
Author: Emmons Sánchez, Ender Enrique <A00963594@itesm.mx>
Subject: Re: Write here your answers to the Discussion Activity


1. Read the section "3. 3-D Homer" which starts in the page 32 of the article. Have you seen the chapter ("Homer3") that is described in that section? YES 2. Answer exercises 1a, 1b and 1c in page 33 of the article. Exercise 1a. Discuss the differences between 2-D and 3-D Homer. be sure to relate shadowing, lighting and physical differences in the 2-D and 3-D worlds to an explanation of how these differences give the appearance of added depth. WELL THE THREE D HOMER IS DARKER, THE YELLOWED SKIN BUDDY DOESN’T APPEAR TO SHINE OR TO BE AS BRIGTH AS IN THE NORMAL WORLD. I THINK THAT WE CAN DEFINE A LOT OF CURVES IN HIS BODY FOR EXAMPLE HIS HEAD REPRESENTS AN ELLIPSOID AND FOR WHAT I’VE SEEN IN OTHER EPISODES I RELATE HIS HEAD MORE TO AN ELLIPSE, EVEN HIS HAIR LOOKS LIKE HALF OF ELLIPSES. HOMER’S STOMACH APPEARS LIKE AN SPHERE IN 3D AND NOT REALLY IN 2D’S WORLD. I BELIEVE THAT MATT GROENING IN THE NORMAL EPISODES USES CONTRASTS OF COLOUR IN THE BACKGROUNDS AND EVEN YOU CAN APPRECIATE IT BECAUSE WHEN SOMEBODY JUMP YOU CAN SEE SHADOW UNDER THEM LIKE IF THEY WERE JUMPING UPWARDS, THE SHADOW IS EFFECTIVE TO CHEAT OUR EYES. Exercise 1b. In the supposedly 2-D world, what aspects could be used to argue that the Simpsons are living in a 2-D world? I’VE ALWAYS LOOKED AT THE MOVEMENTS OF THEIR HANDS AND THEY APPEAR TO RAISE IT AS IF THEY WERE DOING A MOVEMENT TO ANY SIDE, THEY DON’T APPEAR TO RAISE IT ON A Z AXIS. I’VE READ OTHER COMMENTS AND THEY DIDN’T CONVINCE ME OF A 3D SIMPSONS WORLD, SPECIALLY THE ONE OF THE MOE’S TAVERN EXAMPLE. ALL OF THE FORNITURE, THE WALLS AND THE AUTOMOBILES LOOK LIKE IF THEY WERE A BACKGROUND, I’VE NEVER SEEN A VOLUME IN THEM. Exercise 1c. In the supposedly 2-D world, what aspects could be used to argue that they are living in a 3-D world? (Hint: think about their movements and behaviors, the world that is represented, and the use of perspective in the bookcase and in the cube that Professor Prink drew.) WELL SOMETIMES THEY APPEAR TO MOVE OUT OF THE SCREEN AND IN ANOTHER DIRECTION, BUT THAT COULD BE AN EFFECT OF THE SHADOWING AND THE COLORS, ALL THE MOVEMENTS I HAVE APPRECIATED THERE ARE JUST IN TWO DIRECTIONS, I READ ONE COMMENT ON HOW HOMER DRANK A BEER AND I THINK IT ONLY DESCRIBES TWO AXIS, REALLY UPWARDS, DOWNWARDS, AND TO THE SIDES. MAYBE THE CHANGE OF VIEWS FROM THE CAMERA COULD BE A WAY OF SUPPORTING THE 3D IDEA. 3. Answer exercise 2 in page 34 of the article. DEAR MARGE: OOOOUUUUUHHHH! IT ALL LOOKS CREEPY AROUND HERE, I DON’T EVEN KNOW IF I’M ALIVE, I CAN WALK IN THREE DIFFERENT DIRECTIONS AND I SEE A LOT OF SPACE THAT SORROUNDS ME, MY BODY HAS STARTED TO HAVE BALLS OR STRANGE FIGURES IN IT I’M REALLY SCARED MARGE. EVERYTHING IS WEIRD YOU MAY THINK I’M CRAZY OR SOMETHING BUT BELIEVE WHEN I WENT THROUGH THAT WALL I STARTED TO SEE OBJECTS SIMILAR TO THOSE ICE-CREAM COOKIE TRIANGLES THAT WE USE TO PUT THE ICE CREAM BALL UPON THEM (AAAAAHHHHHHHHHHHH! HOW MUCH I WONDER TO HAVE ONE RIGTH NOW) BUT THE DIFFERENCE WAS THAT ITHEY HAD A CIRCLE ABOVE AND THE TRIANGLE BELOW IT WAS FILLED UP WITH A MATERIAL MARGE, CAN YOU IMAGINE IT??? FOR EXAMPLE TAKE A SHEET AND DRAW THE CONE AS YOU KNOW IT, AFTER THAT YOU CAN DRAW A LINE IN THE MIDDLE OF THE TRIANGLE AND THEN IMAGINE THAT THE LINES ON THE TRIANGLE ARE FILLED UP WITH SOMETHING, OR FOR ANOTHER EXAMPLE YOU SHOULD IMAGINE A TREE THAT YOU CAN HOLD OR TOUCH WITH YOUR HAND AND NOT GRAB THE WHOLE SURFACE, I’VE CALLED THIS PROPERTY MARGE THE “VOLUMER” (IN HONOR TO IT’S DISCOVERER). IN OTHER WORD MARGE I SEE A FIGURE THAT IS COMPOSED BY SEVERAL 2D FIGURES. 4. Comment on a four-dimensional Homer, as mentioned in the paragraph that starts at the eleventh row in page 35 of the article. I AGREE WITH THOSE WHO CALLED TIME AN EXTRA DIMENSION BUT IF WE PUT IT IN TERMS OF THE 2D SIMPSON’S THAT I’VE TALKED ABOUT, THEY SHOULD BE THREE DIMENSIONAL BECAUSE WE CAN OBSERVE IT IN THERE TOO, MAYBE A FOURTH DIMENTION IS LOCATED IN THE ATOM OR VERY SMALL THINGS, IF I CAN IMAGINE A HOMER IN 4 DIMENSIONS I WOULD IMAGINE IT MICROSCOPIC, I REMEMBERED THE SUPERSTRINGS THEORY WITH THIS QUESTION. WHY IN A SMALL SIZE I IMAGINE MORE DIMENSIONS???? WELL IMAGINE A ROPE STANDING IN THE SPACE, IF YOU SEE IT FAR, FAR AWAY FROM IT, YOU WILL SEE TWO DIMENSIONS, BUT IF YOU GET CLOSER YOU WILL START TO SEE THE VOLUME OF THE ROPE. 5. Did you know that "The Simpsons" has some allusions to Math and Science? NO, ACTUALLY THE ONLY THING I KNEW ABOUT THEM WAS THAT THEY WANTED TO RECREATE THE LIFE OF AN AMERICAN COMMON FAMILY BUT OBVIUSLY IN A FUNNY WAY, I NEVER THOUGTH THEY HAD TO DEAL WITH SCIENCE TOO. 6. Do you like "The Simpsons"? Why? YES, THEY HAVE FUNNY WAYS TO DESCRIBE ALL OF THE DREAMS OF A PERSON AND THEY SHOW THAT THOSE SORT OF THINGS HAPPENS IN THE REAL LIFE, SOMETIMES YOU IDENTIFY WITH THEM. 7. Do you think that "The Simpsons" is educative? YES, YOU COULD GRAB SOME IDEAS FROM THEM FOR EXAMPLE YOU CAN LEARN NOT TO BE AS HOMER, BE AS LISA, YOU CAN ALSO PICTURE THE REAL WORLD WITH THEM. 8. Compare your answers with the answers of your classmates in the ELECTRONIC DISCUSSION BOARD. Are there other points of view? Do you think they could be right? Why?. FOR WHAT I READ, ALMOST EVERYBODY ASSUMES IT IS A2D WORLD THE ONE OF THE SIMPSON’S, BUT WHEN I READ THE COMMENT OF THE EPISODE WHEN BART AND LISA ENTERS THE TV THEY ARE RIGTH ASSUMING THAT A 3D OBJECT IS SHOWN IN THE TELEVISION. IT IS CONFUSING TO HAVE A LOT OF POINTS OF VIEW, BUT I’M STILL STANDING WITH THE THEORY THAT THEY LIVE IN A 2D WORLD.

Current Forum: The Simpsons	Read 4 times
Date: Fri Aug 20, 2004 3:23 pm
Author: Macias Torres, Luis Armando <A00466819@itesm.mx>
Subject: Re: Write here your answers to the Discussion Activity


1. Yes I’ve seen the chapter. 2.1.a - First difference betwen the 2-D world and 3-D world is the z-axis. Because of this axis we can see solid figures in space, Homer in this chapter appear to be a figure in the 3-D plane because of the shadowing and lighting, it gave to Homer a tri-dimensional appearance and volume, cause Homer appear to be made of spheres and basic figures. 2.1.b- The fact that, they actually were surprised when they knew about a third dimension. They couldn’t understand the concept of the third dimension, because they have been living in only two dimensions all life. 2.1.c- Because they can move through the kitchen, the living room, etc.. and they can hide under an object (in this case, the dog and the cat were under a couch), Homer can go around the armchair. 3.2- Letter Hello March! This place is strange, don’t know were I am but I’m going to explain how is this place: I see some figures that I’ve never seen before, like this thing that seems to be a triangle but it has three more surfaces, two more of the same size and the other one that is another triangle but smaller. I also see something like a circle but with some strange shadow and light around it. Well from the things that I know, I suppose that I’m in another plane… the 3D plane, if we added an axis to our world we obtain a third dimension, to us a circle equation would be x2+y2=r2 but here the “circle” that I mentioned before it seems to have a third axis of coordinates and the equation of this object would be something like this x2+y2+z2=r2 including the new z-axis. Well that’s all I can say about this place March, it’s horrible this place, please help me! 4. I think that four dimensional Homer would be the same Homer but including the time that he appear, like the professor said in class: If this object appear only 1/10000000 second, how would you know if this object was real? How do you know if this object really exist? This object not only depend on volume or surface, it depends on permanency in time too. 5. I really don’t have idea! Well I suppose I didn’t know that because I did not put sufficient attention to the mathematical explanations in the simpsons. 6. Yes, because watching them you can pass the time and you really get fun with them, in addition that you can always talk to somebody about them of any theme. 7. I don’t think so, because they are more like a critic to the society than an educative tv series. 8. I agree with several of my companions that the simpsons are in two dimensions, that´s because you can draw them in paper, but you can’t touch them in the screen. I think too that they represents a three dimensional world in a two dimensional world, and this because they can go around the bed for example.

Current Forum: The Simpsons	Read 2 times
Date: Fri Aug 20, 2004 9:18 pm
Author: Correa Guerrero, Cynthia Aida <A00468008@itesm.mx>
Subject: Re: Write here your answers to the Discussion Activity


1 Read the section "3-D Homer" which starts in the page 32 of the article. Have you seen the chapter that is described in that section?  Yes, I have seen the episode quite a long time ago, so I cannot remember every detail. 2 Answer exercises 1a, 1b and 1c in page 33 of the article.  3D Homer is a more detailed character with a rendering that provides lightning and shadowing effects giving the appearance of three dimensions even in a two-dimensional plane such as a television screen. This rendering provides a sense of depth which causes the effect. Representations of 3D objects in two-dimensional planes rely in the shadow effects to create a sense of nearness of certain objects to show that the other elements of the scene are not in the same distance from every other. Also 3D objects require rounder shapes to denote the depth of them in the plane, while 2D objects don’t need that as they don’t have that sense of distance to be established. There are certain details that may represent a 2D world as the shapes have short sense of lightning and shadowing. The bases of the show are plane figures that move in many times in a single plane, but that is hard to prove when some characters are placed behind or in front others, or moving in an imaginary x-axis perpendicular to the scene. Many objects represent bodies: books, glasses, and the car are just examples of some perspective introduced by the designers. This perspective represents bodies with three dimensions (height, width, depth) that are introduced by lines indicating depth. 3  Answer exercise 2 in page 34 of the article.  Marge, this is a bizarre world, everything looks so much different. My head is not longer as you saw me… it more like a cylinder, imagine you draw a head in front of mine and join every point with the equivalent one, it’s weird. Every shape that existed in our world seems to be propagated to somewhere I haven’t seen before. There some shadows I’ve never seen before, lightning seems not to be getting to every point because of interruption in the straight path it is supposed to be following. 4  Comment on a four-dimensional Homer, as mentioned in the paragraph that starts at the eleventh row in page 35 of the article.  This situation is so much easy to imagine, as it would be the case if something similar happened in our world. It is difficult to imagine a 4th dimension, but it would represent some kind of growth into a plane we have not considered, that provides surfaces when cutting it around the fourth axis. It would be an extended Homer that gave normal Homer representations when cut around the fourth axis. 5 Did you know that "The Simpsons" has some allusions to Math and Science?  I have seen some of the presented concepts but I was not aware of the certainty of them and the uses in Mathematics’ teaching. 6 Do you like "The Simpsons"? Why?  I do like them, because it is light comedy that relieves some tension from our lives. Clever jokes and smart critiques to everyday activities is a fun way to front our world. 7 Do you think that "The Simpsons" is educative?  After reading the article and analyzing the situations, the way some concepts are introduced may be quite useful for introducing taste for Math in every student, from beginning to advanced. This kind of techniques takes the boring side from learning and makes it easy to understand. 8 Compare your answers with the answers of your classmates in the ELECTRONIC DISCUSSION BOARD. Are there other points of view? Do you think they could be right? Why?  I’ve noticed in much of the messages that we had all seen the different formulas and science explanations, but we were not aware of the certainty and importance they are taking in Mathematics teaching. Other similarity is that we all have certain concern about the critique for American society, and that is one of the main attractive spots of the show mentioned by some classmates. Professor, thank you for understanding :).